Besanko and Braeutigam, CH 12
Western University
First-Degree Price Discrimination: Making the Most from Each Consumer
Second-Degree Price Discrimination: Quantity Discounts
Third-Degree Price Discrimination: Different Prices for Different Market Segments
Tying (Tie-In Sales), Bundling
Advertising
A monopolist charges a uniform price if it sets the same price for every unit of output sold
While the monopolist captures profits due to an optimal uniform pricing policy
A firm with market power may be able to increase its profits by charging more than one price for its product through price discrimination
A policy of first-degree (or perfect) price discrimination prices each unit sold at the consumer’s maximum willingness to pay
A policy of second-degree price discrimination allows the monopolist to offer consumers a quantity discount
A policy of third-degree price discrimination offers a different price for each segment of the market (or each consumer group) when membership in a segment can be observed
Certain market features must be present for a firm to capture more surplus with price discrimination:
The demand curve is the willingness to pay curve
Since the demand curve slopes downward, the consumer buying the first unit is willing to pay a higher price than the consumer buying the second unit
If the seller can perfectly implement first-degree price discrimination, it will price each unit at the maximum amount the consumer of that unit is willing to pay
The producer sells each unit to the consumer with the highest reservation price for that unit, at that price
The monopolist will continue selling units until the reservation price exactly equals the marginal cost
The producer captures all the surplus and there is no deadweight loss
Perfect first-degree price discrimination therefore leads to an economically efficient level of output!
In the real world, it is harder to learn about willingness to pay
If you ask a customer about her willingness to pay, she will not reveal her reservation price
Suppose a monopolist has a constant marginal cost MC = 2 and faces the demand curve P = 20 − Q
Uniform pricing surplus?
First-degree price discrimination surplus?
With uniform pricing, \(MR=P+\frac{dP}{dQ}Q\)
With perfect first-degree price discrimination, only the first effect is present
When the firm sells one more unit, it does not have to reduce its price on all the other units it is already selling
So the marginal revenue curve with first-degree price discrimination is just \(MR = P\)
The marginal revenue curve equals the demand curve
A policy of second-degree price discrimination allows the monopolist to charge a different price to different consumers
While different consumers pay different prices, the reservation price of any one consumer cannot be directly observed
Sellers know that each customer’s demand curve for a good is typically downward-sloping
A seller may use this information to capture extra surplus by offering quantity discounts to consumers
Not every form of quantity discounting represents price discrimination. Often sellers offer quantity discounts because it costs them less to sell a larger quantity
One distinguishing feature of second-degree price discrimination is that the amount consumers pay for the good or service actually depends on two or more prices (parts)
For example, telecommunication services work under a multipart tariff: a subscription charge plus a usage charge
If a consumer pays one price for one block of output and another price for another block of output, the consumer faces a block tariff
Firm’s objective is to maximize profits by choosing the optimizing quantity at each block (therefore looking for the optimal block price)
The monopolist might capture additional surplus by offering a quantity discount
Charge a price for the first units (11) and a lower price (8) for any additional units
What’s the optimal block tariff?
Show mathematically on the board
Consumer’s average expenditure, average outlay, is total expenditure \(E\) divided by total quantity \(Q\)
In our previous example, \[ E = \begin{cases} \$14Q, & \text{if } Q \leq 6 \\ \$84 + \$8(Q-6), & \text{if } Q > 6 \end{cases} \]
So, the consumer’s average outlay is \[ \frac{E}{Q} = \begin{cases} \$14, & \text{if } Q \leq 6 \\ \frac{\$84 + \$8(Q-6)}{Q}, & \text{if } Q > 6 \end{cases} \]
Second Degree Price Discrimination results in a non-linear outlay schedule
Self Selection
Pareto superior allocation
\[ T=F+rQ \]
This, effectively, charges demanders of a low quantity a different average price than demanders of a high quantity
Example: include hook-up charge plus usage fee for a telephone, club membership, and so on
All customers are identical
P = 100 - Q
MC = AC = 10
What is the optimal two-part tariff?
Two steps: Draw graph on the board
Maximize the benefits to the consumers by charging r = MC = 10
Capture this benefit by setting F = consumer benefits = 4050
Any higher usage charge would result in a dead-weight loss that could not be captured by the monopolist
Any lower usage charge would result in selling at less than marginal cost
In essence, the monopolist maximizes the surplus, then sets the lump sum fee to capture the entire surplus for itself
The total surplus captured is the same as in the case of perfect price discrimination
Demand differs from one consumer to the next. High subscription and usage tariffs might capture more surplus from large-demand consumers, but small-demand consumers will not buy the service at all
The firm cannot tell apart large from small-demand consumers. Firms need to offer customers a menu of subscription and usage charges to incentivize them to self-select
If a firm can identify different consumer groups, or segments, in a market and can estimate each segment’s demand curve, the firm can practice third-degree price discrimination by setting a profit-maximizing price for each segment
Example: Movie ticket sales to senior citizens or students at a discount
How does a monopolist maximize profit with this type of price discrimination?
The optimal pricing maximizes the monopolist’s profits \[ \max_{Q_1,Q_2} P_1(Q_1)Q_1 + P_2(Q_2)Q_2- C(Q_1+Q_2) \]
\(P_i(Q_i)\) denote the inverse demand curves of group \(i\)
The optimal solution must have \[ \begin{aligned} MR_1(Q_1)&=MC(Q_1+Q_2) \\ MR_2(Q_2)&=MC(Q_1+Q_2) \end{aligned} \]
In other words, the monopolist maximizes total profits by maximizing profits from each group individually
Since marginal cost is the same in each market, \(MR_1=MR_2=MC\)
Otherwise, the monopolist could raise revenues by switching sales from the low MR group to the high MR group
Note that the price is higher in the lower elasticity demand than in the high elasticity demand
A firm that price discriminates will set a low price for the price-sensitive group and a high price for the group that is relatively price-insensitive
Senior citizens and students are more likely to be price-sensitive than the average consumer
Show mathematically on the board
Sorting consumers based on a consumer characteristic that
the firm can see (such as age or status) and
is strongly related to a consumer characteristic that the firm cannot see but would like to observe (such as willingness to pay or elasticity of demand)
MC = AC = 20
P1 = 100 - Q1
P2 = 80 - 2Q2
MR1 = 100 - 2Q1 = MC = 20
MR2 = 80 - 4Q2 = MC = 20
Q1* = 40
Q2* = 15
P1* = 60
P2* = 50
Inverse elasticity pricing
Capacity constraints
A tie-in sale occurs if a customer can buy one product only if they agree to purchase another product as well
Requirements tie-in sales occur when a firm requires customers who buy one product from the firm to buy another product from the firm
A requirements tie-in sale may be used in place of price discrimination when the firm cannot observe the relative willingness to pay of different customers
Package tie-in sales (or bundling) occur when goods are combined so that customers cannot buy either good separately
Bundling may be used in place of price discrimination to increase producer surplus when consumers have different willingness to pay for the goods sold in the bundle
But bundling does not always pay
Without bundling: pc = $1500 pm = $600
Profit cm = $800
With bundling: pb = $1800
Profit b = $1000
Without bundling: pc = $1500
pm = $600
Profit cm = $800
With bundling: pb = $2100
Profit b = $800
In general, bundling a pair of goods only pays if their demands are negatively correlated
Customers who are willing to pay relatively more for good A are not willing to pay as much for good B
The reason is that the price is determined by the purchaser with the lowest reservation price
If reservation prices for the two goods are negatively correlated, bundling reduces the dispersion of reservation prices and so raises the price at which additional units can be sold
The firm can capture surplus using nonprice strategies such as advertising
When the firm does not advertise, its maximum profit is areas I + II
When the firms spends A1 dollars on advertising, its maximum profit is areas II + III